String Phenomenology

Introduction Model Building Moduli Stabilisation Flavour Problem

Joseph Conlon (Oxford University)

EPS HEP Conference, Krakow July 17, 2009

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Chalk and Cheese?

Figure: String theory and phenomenology?

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem String Theory

◮ String theory is where one is led by studying quantised relativistic strings. ◮ It encompasses lots of areas ( black holes, quantum ﬁeld theory, quantum gravity, mathematics, particle physics....) and is studied by lots of diﬀerent people. ◮ This talk is on string phenomenology - the part of string theory that aims at connecting to the Standard Model and its extensions. ◮ It aims to provide a (brief) overview of this area. (cf Angel Uranga’s plenary talk)

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem String Theory

◮ For technical reasons string theory is consistent in ten dimensions. ◮ Six dimensions must be compactiﬁed. ◮ Ten = (Four) + (Six)

◮ Spacetime = (M4) + Calabi-Yau Space ◮ All scales, matter, particle spectra and couplings come from the geometry of the extra dimensions. ◮ All scales, matter, particle spectra and couplings come from the geometry of the extra dimensions.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Model Building

Various approaches in string theory to realising Standard Model-like spectra: ◮ E8 E8 heterotic string with gauge bundles × ◮ Type I string with gauge bundles ◮ IIA/IIB D-brane constructions ◮ Heterotic M-Theory ◮ M-Theory on G2 manifolds

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Heterotic String

Start with an E8 vis E8 hid gauge group in ten dimensions. , × , The gauge group is broken and chiral matter generated by an appropriate choice of gauge ﬁeld in the Calabi-Yau.

E8 vis E8 hid SU(5)vis E8 hid , E6 vis E8 hid , × , → × , , × , Further Wilson lines are needed to break to the Standard Model. Requires a holomorphic, stable vector bundle in order to carry out the breaking. At a technical level, requires the mathematics of bundle stability (James Gray’s talk).

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Heterotic String

aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbCY aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb M4 x aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbFMN abaaaaaaaaaaaaaaabbbbbbbbbbbbbbb

Schematic of heterotic compactiﬁcation: the gauge bundle FMN breaks the E8 E8 gauge group and sources chiral zero modes, × which extend throughout the bulk space.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Heterotic String

Weakly coupled heterotic string is a global construction. Gauge ﬁelds propagate on the bulk of the Calabi-Yau.

1 MP αGUT , Ms . ∼ ∼ √ V V String scale is necessarily close to the Planck scale. Possible to construct models with Standard Model spectra, and many more with Standard-Model like spectra.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem D-brane constructions

Solitonic objects (D-branes) carry worldvolume gauge ﬁelds. Intersections of two D-branes give chiral matter on the intersection. Models of intersecting D-branes can give non-abelian gauge groups with chiral matter and may provide a basis for realising the Standard Model. Stability of D-branes requires classifying special Lagrangian cycles/coherent sheaves on a Calabi-Yau. D-brane constructions lead to non-GUT approaches to reconstructing the Standard Model spectrum.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem D-brane constructions

aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbCY aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb(N,M) M4 x aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb abaaaaaaaaaaaaaaabbbbbbbbbbbbbbb U(N) U(M)

Schematic of IIA D-brane compactiﬁcation: D-branes wrap geometric cycles in the Calabi-Yau and chiral matter is supported on D-brane intersections.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem D-brane constructions

◮ Strength of gauge group is determined by volume of cycle Σi wrapped by D-brane:

1 MP αi , Ms . ∼ Vol(Σi ) ∼ Vol(CY )

◮ As Vol(Σi ) and Vol(CY ) are not necessarilyp connected, string scale can be much lower than the Planck scale. ◮ Can imagine Standard Model constructions with string scales close to the TeV scale.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem F-theory constructions

◮ An extension of D-brane constructions which includes certain non-perturbative eﬀects. ◮ Branes are geometrised as the singularities of an 8-dimensional space: includes D-branes and also further exceptional branes. ◮ Shares properties of brane constructions such as localisation of gauge groups, but also naturally allows for the possibility of GUT models. ◮ Can also the string scale to be much lower than the Planck scale. ◮ But what determines the string scale? Moduli −→ stabilisation

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation

Strings are compactiﬁed on Calabi-Yau manifolds.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation

Geometric deformations of Calabi-Yau manifolds appear as (naively) massless scalars in 4 dimensions. Calabi-Yaus have two basic deformations: ◮ K¨ahler (size) deformations: modifying the K¨ahler form J = ti ωi of the Calabi-Yau. ◮ ComplexP structure (shape) deformations modifying the complex structure of the Calabi-Yau.

K¨ahler deformations are counted by h1,1( ) and complex 2M1 structure deformations are counted by h , ( ). M

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation

It is necessary to give masses to moduli to avoid ﬁfth forces bounds. The process of moduli stabilisation is also closely tied to supersymmetry breaking. Moduli stabilisation is best described in the framework of 4-dimensional supergravity. We need to determine the ◮ K¨ahler potential, (Φ, Φ).¯ K ◮ Superpotential, W (Φ). K i¯j 2 Scalar potential is V = e ( Di WD¯W¯ 3 W ) K j − | |

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation

K i¯j 2 V = e ( Di WD¯W¯ 3 W ) K j − | | Moduli potential is a potential for scalar ﬁelds. ◮ Can be used to try and realise inﬂation in string theory. (Marco Zagermann’s talk) ◮ Also is very important for understanding supersymmetry breaking - minima of V can break supersymmetry and generate soft terms. ◮ We look at supersymmetry breaking in more detail.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation (IIB) The K¨ahler potential is

= 2ln (T + T¯ ) ln i Ω Ω(¯ U, U¯ ) ln(S + S¯) K − V − ∧ − Kähler Z dilaton complex structure | {z } | {z } | {z } Three-form fluxes can stabilise the dilaton and complex structure moduli: W = G3 Ω ∧ Z Gives an effective no-scale model: = 2ln (T + T¯ ), K − V W = W0.

Broken supersymmetry and vanishing vacuum energy. Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Moduli Stabilisation (IIB)

Non-perturbative and α′ corrections can ﬁx the remaining T moduli:

ξ = 2ln + 3/2 K − V 2gs !

−ai Ti W = W0 + Ai e . i X Can obtain a minimum at exponentially large values of the volume. Supersymmetry breaking is similar to no-scale and is dominated by the volume modulus (F Ti = 0, F U = 0). 6 So what?

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem

The LHC hopes to discover supersymmetry.

But why should any new susy signatures occur at all?

One major problem:

Why hasn’t supersymmetry been discovered already?

Compare with ◮ The c quark - predicted before discovery through its contribution to FCNCs (the GIM mechanism) ◮ The t quark - mass predicted accurately through loop contributions at LEP I.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem

¯s d¯ δ¯˜ ˜ ¯˜s d¯˜s d¯

g˜ g˜

˜ δ˜ ˜s ¡d d˜s d s

The MSSM gives new contributions to K0 K¯0 mixing. −

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem γ˜

δµ˜e˜ µ e µ˜ µ˜ e˜

γ ¡

The MSSM generates new contributions to BR(µ eγ). →

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem

SUSY is a happy bunny if soft terms are ﬂavour universal.

2 2 mQ,αβ¯ = mQ , Aαβγ = AYαβγ,

φM1 = φM2 = φM3 = φA.

Why should this be?

◮ Answer to flavour problem significantly affects all of susy phenomenology. ◮ This problem cannot be addressed purely within effective field theory - needs UV completion.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem ◮ The flavour problem says that supersymmetry breaking cannot know about flavour physics. ◮ A priori, this is unnatural - why should the susy breaking sector be entirely ignorant of flavour? ◮ String theory can give a natural answer.

The size and shape ﬁelds of the Calabi-Yau are factorised

Φall =ΨKahler χcomplex ⊕ Ψ and χ represent two distinct and decoupled sectors.

= 2ln (T + T¯ ) ln i Ω Ω(¯ U, U¯ ) ln(S + S¯) K − V − ∧ − K¨ahler Z dilaton complexstructure | {z } | {z } | {z } Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem The MSSM Flavour Problem

We have Φall =ΨKahler χcomplex ⊕ with Ψ and χ representing two distinct and decoupled sectors. It turns out that

1. ΨKahler gives rise to supersymmetry breaking.

2. χcomplex generates the ﬂavour structure: Yαβγ = Yαβγ(χ).

Supersymmetry breaking and ﬂavour physics decouple and soft terms are ﬂavour universal! The origin of this decoupling is the geometric properties of Calabi-Yaus.

Joseph Conlon (Oxford University) String Phenomenology Introduction Model Building Moduli Stabilisation Flavour Problem Conclusions

◮ Have provided an overview of the area of string phenomenology ◮ Subject divides into two main areas, model building and moduli stabilisation. ◮ Have also described how Calabi-Yau geometry can give intrinsically stringy solutions to low energy ﬁeld theory problems.

Joseph Conlon (Oxford University) String Phenomenology